To get started using Multiverse, you'll need to download the base program here. Just extract it in its own folder anywhere on your computer. There's no pesky installer.
The first thing you'll need to do is run MultiverseLauncher.jar. The launcher checks for and downloads updates for the program and the card database every time you run it. Since you've never run it before, you most likely need to update.
After it's done updating, you're all set and can do whatever you want! RunDeckEditor.bat starts the deck editor (which is currently incomplete, but still very helpful because its search features all work). You'll just have to type up decklists by hand if none of the built-in ones are to your liking.
You can start a normal server with RunServer.bat, or a draft server with RunDraftServer.bat. Note that the regular server can only be connected to by players on your local area network, and VPNs won't help you. If you want to play with people around the world, get MtGO or Duels of the Planeswalkers. MTG Online also has the most accurate rules engine out there and has tournament support. Anybody can connect to your draft server, but deckbuilding is mostly automated and there is no tournament support (all the players are thrown into one game).
The Interface
The interface is very minimalistic and easy to use. Your hand and mana pool appear in the bottom right of the screen. Above them is a white bar with text over it. This is the priority timer. It drains whenever you get priority and passes for you if you take too long. You can pause it by pressing SPACEBAR.
The Priority Panel appears at the top right of the screen. This is the main way you will navigate through each player's turn during a game. The current step of the turn is always highlighted in green. While it's your turn, you can left-click on any step name to skip to that step. Left-clicking the "Skip All" button ends your turn.
You can right-click any of the step names to set a breakpoint. If a step is breakpointed, it will become red, and the game will stop on that step during each other player's turn and ask you if you want to do anything. Most players will find it useful to stop at the declare blockers step (so they can block) and the end step, so they can cast instants and use abilities before their opponent's turn ends.
By default, the game gives priority to every player when something is on the stack. You can right-click the "Skip All" button to automatically pass priority on everything. You should only do this if you have nothing to do during other players' turns. Even with "Skip-All" turned on, the game will still stop for you at whatever breakpoints you have set.
The Stack appears as a pile of cards in the middle of the screen (or, when something is being added to it, on the side of the screen). Right-clicking on an object on the stack will make you pass priority until that object resolves (or is otherwise removed from the stack). This can be very useful when there are a lot of triggered abilities stacking up and you want to resolve them all without clicking a million times.
You can move the camera around by using the numpad arrow keys (numpad 2, 4, 6, and 8). Numpad 9 and 3 zoom in and out, respectively. You can zoom-in on any card with the mouse wheel to see its full text and additional details.
Combat
To attack a player, make sure you are in the Declare Attackers (action) step. First, click on the player you wish to attack, then click on all the creatures you wish to attack with. You can un-declare an attacker by clicking on it again.
To block, first click on an attacking creature. Then, click any number of creatures you want to block with. It's done this way to support creatures that can block multiple attackers.